Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5118)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-14/3, b>=a

For fixed z and a=-14/3, b=-13/3

http://functions.wolfram.com/07.23.03.5118.01

Input Form

Hypergeometric2F1[-(14/3), -(13/3), 5/2, -z] == (27 (Sqrt[z] (-262144 + 209854281 z - 1259303991 z^2 + 673503640 z^3 + 1379483256 z^4 - 714907680 z^5 + 48533120 z^6) Cosh[ArcSinh[Sqrt[z]]/3] + 3 Sqrt[1 + z] (262144 + 18874368 z - 495351105 z^2 + 1854564584 z^3 - 1789519608 z^4 + 455633760 z^5 - 21015680 z^6) Sinh[ArcSinh[Sqrt[z]]/3]))/ (6177770675 z^(3/2) Sqrt[1 + z])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]